Download Real-time detection of single-electron tunneling using a quantum

APPLIED PHYSICS LETTERS
VOLUME 85, NUMBER 19
8 NOVEMBER 2004
Real-time detection of single-electron tunneling using a quantum point
contact
L. M. K. Vandersypen,a) J. M. Elzerman, R. N. Schouten, L. H. Willems van Beveren,
R. Hanson, and L. P. Kouwenhoven
Kavli Institute of NanoScience and ERATO Mesoscopic Correlation Project, Delft University of Technology,
Lorentzweg 1, 2628 CJ Delft, The Netherlands
(Received 12 July 2004; accepted 22 September 2004)
We observe individual tunnel events of a single electron between a quantum dot and a reservoir,
using a nearby quantum point contact (QPC) as a charge meter. The QPC is capacitively coupled to
the dot, and the QPC conductance changes by about 1% if the number of electrons on the dot
changes by one. The QPC is voltage biased and the current is monitored with a current–voltage
共I – V兲 convertor at room temperature. We can resolve tunnel events separated by only 8 ␮s, limited
by noise from the I – V convertor. Shot noise in the QPC sets a 25 ns lower bound on the accessible
timescales. © 2004 American Institute of Physics. [DOI: 10.1063/1.1815041]
Fast and sensitive detection of charge has greatly propelled the study of single-electron phenomena. The most
sensitive electrometer known today is the single-electron
transistor (SET),1 incorporated into a radio-frequency (rf)
resonant circuit.2 Such rf-SETs can be used, for instance, to
detect charge fluctuations on a quantum dot, capacitively
coupled to the SET island.3,4 Already, real-time electron tunneling between a dot and a reservoir has been observed on a
sub-␮s timescale.3
A much simpler electrometer is the quantum point contact (QPC). The conductance, GQ, through the QPC channel
is quantized, and at the transitions between quantized conductance plateaus, GQ is very sensitive to the electrostatic
environment, including the number of electrons, N, on a dot
in the vicinity.5 This property has been exploited to measure
fluctuations in N in real time, on a timescale from seconds
(Ref. 6) down to about 10 ms.7
Here, we demonstrate that a QPC can be used to detect
single-electron charge fluctuations in a quantum dot in less
than 10 ␮s, and analyze the fundamental and practical limitations on sensitivity and bandwidth.
The quantum dot and QPC are defined in the twodimensional electron gas (2DEG) formed at a
GaAs/ Al0.27Ga0.73As interface 90 nm below the surface, by
applying negative voltages to metal surface gates [Fig. 1(a)].
The device is attached to the mixing chamber of a dilution
refrigerator with a base temperature of 20 mK, and the electron temperature is ⬃300 mK in this measurement. The dot
is set near the N = 0 to N = 1 transition, with the gate voltages
tuned such that the dot is isolated from the QPC drain, and
has a small tunnel rate, ⌫, to the reservoir. Furthermore, the
QPC conductance is set at GQ = 1 / RQ ⬇ 共30 k⍀兲−1, roughly
halfway the transition between GQ = 2e2 / h and GQ = 0, where
it is most sensitive to the electrostatic environment.9
A schematic of the electrical circuit is shown in Fig.
1(b). The QPC source and drain are connected to roomtemperature electronics by signal wires, which run through
Cu-powder filters at the mixing chamber to block highfrequency noise 共⬎100 MHz兲 coming from room temperature. Each signal wire is twisted with a ground wire from
a)
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room temperature to the mixing chamber. A voltage, Vi, is
applied to the source via a home-built optocoupled isolation
stage. The current through the QPC, I, is measured via a
current–voltage 共I – V兲 convertor connected to the drain, and
an optocoupled isolation amplifier, both home built as well.
The I – V convertor is based on a dual low-noise junction
field effect transistor (JFET) (Interfet 3602). Finally, the signal is ac coupled to an eighth-order elliptic low-pass filter
(SRS650), and the current fluctuations, ⌬I, are digitized at
2.2⫻ 106 14-bit samples per second (ADwin Gold).
The measurement bandwidth is limited by the low-pass
filter formed by the capacitance of the line and Cu-powder
FIG. 1. (a) Scanning electron micrograph of a device as used in the experiment (gates which are grounded are hidden). Gates T, M, and R define the
quantum dot (dotted circle), and gates R and Q form the QPC. Gate P is
connected to a pulse sourcevia a coaxial cable (see Ref. 8 for a more detailed description). (b) Schematic of the experimental setup, including the
most relevant noise sources. The QPC is represented by a resistor, RQ. (c)
Noise spectra measured when the I – V convertor is connected to the sample
(top solid trace), and, for reference, to an open-ended 1 m twisted pair of
wires (lower solid trace). The latter represents a 300 pF load, if we include
the 200 pF measured amplifier input capacitance. The diagram also shows
the calculated noise level for the 300 pF reference load, neglecting IA
(dotted–dashed), and the shot noise limit (dashed). The left and right axes
express the noise in terms of current through the QPC and electron charge
on the dot respectively.
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© 2004 American Institute of Physics
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Vandersypen et al.
Appl. Phys. Lett., Vol. 85, No. 19, 8 November 2004
4395
TABLE I. Contributions to the noise current at the I – V convertor input. By
dividing the noise current by 300 pA (the signal corresponding to one electron charge leaving the dot), we obtain the rms charge noise on the dot.
rms noise current
Noise
source
ISN
VT
VA
VA, low f
VA, high f
IA
Expression
冑T共1 − T兲2eI
冑4kBT / RFB
VA 1 + j2␲ fRQCL RQ
VA / RFB
VA2␲ fCL
IA
Ⲑ
rms charge noise
A / 冑Hz
e / 冑Hz
49⫻ 10−15
41⫻ 10−15
1.6⫻ 10−4
1.4⫻ 10−4
32⫻ 10−15
7.5⫻ 10−18 f
¯
1.1⫻ 10−4
2.5⫻ 10−8 f
¯
filters, CL ⬇ 1.5 nF, and the input impedance of the I – V convertor, Ri = RFB / A. Thermal noise considerations (below) impose RFB = 10 M⍀. We choose the amplifier gain A = 10 000,
such that 1 / 共2␲RiCL兲 ⬇ 100 kHz.10 However, we shall see
that the true limitation to measuring speed is not the bandwidth but the signal-to-noise ratio as a function of frequency.
The measured signal corresponding to a single-electron
charge leaving the dot amounts to ⌬I ⬇ 0.3 nA with the QPC
biased at Vi = 1 mV, a 1% change in the overall current I (I
⬇ 30 nA, consistent with the series resistance of RQ, Ri
= 1 k⍀ and the resistance of the Ohmic contacts of about
2 k⍀). Naturally, the signal strength is proportional to Vi, but
we found that for Vi 艌 1 mV, the dot occupation was affected, possibly due to heating. We therefore proceed with
the analysis using I = 30 nA and ⌬I = 0.3 nA.
The most relevant noise sources11 are indicated in the
schematic of Fig. 1(b). In Table I, we give an expression and
value for each noise contribution in terms of root-meansquare (rms) current at the I – V convertor input, so it can be
compared directly to the signal, ⌬I. We also give the corresponding value for the rms charge noise on the quantum dot.
Shot noise, ISN, is intrinsic to the QPC and therefore unavoidable. Both ISN and ⌬I are zero at QPC transmission T
= 0 or T = 1, and maximal at T = 1 / 2; here, we use T 艋 1 / 2.
The effect of thermal noise, VT, can be kept small compared
to other noise sources by choosing RFB sufficiently large;
here RFB = 10 M⍀. The JFET input voltage noise is measured
to be VA = 0.8 nV/ 冑Hz. As a result of VA, a noise current
flows from the I – V convertor input leg to ground, through
the QPC in parallel with the line capacitance. Due to the
capacitance, CL, the rms noise current resulting from VA increases with frequency; it equals ⌬I at 120 kHz. There is no
specification available for the JFET input current noise, IA,
but for comparable JFETs, IA is a few fA/ 冑Hz at 1 kHz.
We summarize the expected noise spectrum in Fig. 1(c),
and compare this with the measured noise spectrum in the
same figure. For a capacitive reference load CL = 300 pF, the
noise level measured below a few kHz is 52 fA/ 冑Hz, close
to the noise current due to VT, as expected. At high frequencies, the measured noise level is significantly higher than
would be caused by VA in combination with the 300 pF load,
so it appears that IA rapidly increases with frequency. With
the sample connected, we observe substantial 1 / f 2 noise (1 / f
in the noise amplitude), presumably from spurious charge
fluctuations near the QPC, as well as interference at various
frequencies. Near 100 kHz, the spectrum starts to roll off
because of the 100 kHz low-pass filter formed by CL
FIG. 2. (Color online) Measured changes in the QPC current, ⌬I, with the
electrochemical potential in the dot and in the reservoir nearly equal. ⌬I is
“high” and “low” for 0 and 1 electrons on the dot respectively (Vi = 1 mV;
the steps in ⌬I are ⬇0.3 nA). Traces are offset for clarity. (a) The dot
potential is lowered from top to bottom. (b) The tunnel barrier is lowered
from top to bottom.
= 1.5 nF and Ri = 1 k⍀ (for the reference load, CL is only
300 pF so the filter cutoff is at 500 kHz).
From the data, we find that the measured charge noise
integrated from dc is about three times smaller than e at
40 kHz. We set the cutoff frequency of the external low-pass
filter at 40 kHz, so we should see clear steps in time traces of
the QPC current, corresponding to single electrons tunneling
on or off the dot.
We test this experimentally, in the regime where the
electrochemical potential in the dot is nearly lined up with
the electrochemical potential in the reservoir. The electron
can then spontaneously tunnel back and forth between the
dot and the reservoir, and the QPC current should exhibit a
random telegraph signal (RTS). This is indeed what we observe experimentally (Fig. 2). In order to ascertain that the
RTS really originates from electron tunnel events between
the dot and the reservoir, we verify that: (1) The dot potential
relative to the Fermi level determines the fraction of the time
an electron resides in the dot [Fig. 2(a)] and (2) the dot–
reservoir tunnel barrier sets the RTS frequency [Fig. 2(b)].
The rms baseline noise is ⬃0.05 nA and the shortest steps
that clearly reach above the noise level are about 8 ␮s long.
This is consistent with the 40 kHz filter frequency, which
permits a rise time of 8 ␮s.
Next, we induce tunnel events by pulsing the dot potential, so N predictably changes from 0 to 1 and back to 0. The
response of the QPC current to such a pulse contains two
contributions [Fig. 3(a)]. First, the shape of the pulse is reflected in ⌬I, as the pulse gate couples capacitively to the
QPC. Second, some time after the pulse is started, an electron tunnels into the dot and ⌬I goes down by about 0.3 nA.
Similarly, ⌬I goes up by 0.3 nA when an electron leaves the
dot, some time after the pulse ends. We observe that the time
FIG. 3. (a) Measured changes in the QPC current, ⌬I, when a pulse is
applied to gate P, near the degeneracy point between 0 and 1 electrons on
the dot 共Vi = 1 mV兲. (b) Average of 286 traces as in (a). The top and bottom
panel are taken with a different setting of gate M. The damped oscillation
following the pulse edges is due to the eighth-order 40 kHz filter.
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4396
Vandersypen et al.
Appl. Phys. Lett., Vol. 85, No. 19, 8 November 2004
before tunneling takes place is randomly distributed, and obtain a histogram of this time simply by averaging over many
single-shot traces [Fig. 3(b)]. The measured distribution decays exponentially with the tunnel time, characteristic of a
Poisson process. The average time before tunneling corresponds to ⌫−1, and can be tuned by adjusting the tunnel barrier.
Our measurements clearly demonstrate that a QPC can
serve as a fast and sensitive charge detector. Compared to an
SET, a QPC offers several practical advantages. First, a QPC
requires fabrication and tuning of just a single additional gate
when integrated with a quantum dot defined by metal gates,
whereas an SET requires two tunnel barriers, and a gate to
set the island potential. Second, QPCs are more robust and
easy to use in the sense that spurious low-frequency fluctuations of the electrostatic potential hardly change the QPC
sensitivity to charges on the dot (the transition between
quantized conductance plateaus has an almost constant slope
over a wide range of electrostatic potential), but can easily
spoil the SET sensitivity.
With a rf-SET, a sensitivity to charges on a quantum dot
of ⬃2 ⫻ 10−4e / 冑Hz has been reached over a 1 MHz
bandwidth.3 Theoretically, even a ten times better sensitivity
is possible.2 Could a QPC perform equally well?
The noise level in the present measurement could be
reduced by a factor of 2–3 using a JFET input stage which
better balances input voltage noise and input current noise.
Further improvements can be obtained by lowering CL, either by reducing the filter capacitance, or by placing the I – V
convertor closer to the sample, inside the refrigerator. The
bandwidth would also increase as it is inversely proportional
to CL.
Much more significant reductions in the instrumentation
noise could be realized by embedding the QPC in a resonant
electrical circuit and measuring the damping of the resonator,
analogous to the operation of a rf-SET. We estimate that with
an “rf-QPC” and a low-temperature high electron mobility
transistor amplifier, the sensitivity could be 2 ⫻ 10−4e / 冑Hz.
At this point, the noise current from the amplifier circuitry is
comparable to the QPC shot noise. Furthermore, the bandwidth does not depend on CL in reflection measurements, and
can easily be 1 MHz.
To what extent the signal can be increased is unclear, as
we do not yet understand the mechanism through which the
dot occupancy is disturbed for Vi ⬎ 1 mV.12 Certainly, the
capacitive coupling of the dot to the QPC channel can easily
be made five times larger than it is now by optimizing the
gate design.6 Keeping Vi = 1 mV, the sensitivity would then
be 4 ⫻ 10−5e / 冑Hz.
Finally, we point out that, unlike a SET, a QPC can reach
the quantum limit of detection,13 where the measurementinduced decoherence takes the minimum value permitted by
quantum mechanics. Qualitatively, this is because: (1) information on the charge state of the dot is transferred only to the
QPC current and not to degrees of freedom which are not
observed, and (2) an external perturbation in the QPC current
does not couple back to the charge state of the dot.
The authors thank R. Schoelkopf, K. Schwab, K. Harmans, and L. Saminadayar for useful discussions, T.
Fujisawa, T. Hayashi, T. Saku, and Y. Hirayama for help with
device fabrication, and the DARPA-QUIST program, the
ONR, the EU-RTN network on spintronics, and the Dutch
Organization for Fundamental Research on Matter (FOM)
for financial support.
1
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Prober, Science 280, 1238 (1998).
3
W. Lu, Z. Ji, L. Pfeiffer, K. W. West, and A. J. Rimberg, Nature (London)
423, 422 (2003).
4
T. Fujisawa, T. Hayashi, Y. Hirayama, H. D. Cheong, and Y. H. Jeong,
Appl. Phys. Lett. 84, 2343 (2004).
5
M. Field, C. G. Smith, M. Pepper, D. A. Richie, J. E. F. Frost, G. A. C.
Jones, and D. G. Hasko, Phys. Rev. Lett. 70, 1311 (1993).
6
J. Cooper, C. G. Smith, D. A. Ritchie, E. H. Linfield, Y. Jin, and H.
Launois, Phys. E 6, 457 (2000).
7
R. Schleser, E. Ruh, T. Ihn, K. Ennslin, D. C. Driscoll, and A. C. Gossard,
cond-mat/0406568.
8
J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren,
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9
Despite a B = 10 T field in the plane of the 2DEG, no spin–split plateau in
the QPC conductance is visible in this sample.
10
The bandwidth of the amplifier inside the I – V convertor is 500 kHz, and
the output ISO-amp bandwidth is 300 kHz.
11
P. Horowitz and W. Hill, The Art of Electronics (Cambridge University
Press, Cambridge, UK, 1989).
12
The statistics of the RTS was altered for Vi ⬎ 1 mV, irrespective of: (1)
Whether Vi was applied to the QPC source or drain, (2) the potential
difference between the reservoir and the QPC source/drain, and (3) the
QPC transmission T.
13
A. N. Korotkov, Phys. Rev. B 60, 5737 (1999); A. A. Clerk, S. M. Girvin,
and A. D. Stone, ibid. 67, 165324 (2003).
2
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